Simple Circuit Equivalents for the Constant Phase Element

TL;DR

This paper demonstrates that the constant phase element's behavior can be exactly modeled by simple RL and RC circuits with linearly increasing component values, clarifying its physical interpretation.

Contribution

It introduces a novel equivalence between the CPE and simple time-varying circuit models, providing a clearer physical understanding of the CPE.

Findings

CPE responses match those of RL and RC circuits with linearly increasing components

Step and impulse responses are derived and verified by simulation

Time-varying component realization aligns with known application properties

Abstract

The constant phase element (CPE) with a frequency-independent negative phase between current and voltage is used extensively in e.g. the bioimpedance and electrochemistry fields. Its physical meaning is only partially understood. Here we show that the responses of both the common capacitive CPE as well as the inductive CPE are exactly the same as those of simple RL and RC circuits where the inductor's or capacitor's value increases linearly with time. The resulting step and impulse responses are found and verified by simulation with the Micro-Cap simulation program. The realization with time-varying components correlates with known time-varying properties in applications.